#chisq为卡方分布函数
chif <- function(x, df) {
  dchisq(x, df = df)
}

##卡方分布 df=1,2, 4, 6 and 10
curve(chif(x, df = 1), 0, 20, ylab = "p(x)", lwd = 2)
curve(chif(x, df = 2), 0, 20, col = 2, add = T, lty = 2, lwd = 2)
curve(chif(x, df = 4), 0, 20, col = 3, add = T, lty = 3, lwd = 2)
curve(chif(x, df = 6), 0, 20, col = 4, add = T, lty = 4, lwd = 2)
curve(chif(x, df = 10), 0, 20, col = 5, add = T, lty = 5, lwd = 2)
legend("topright", legend = c("df=1", "df=2", "df=4", "df=6", "df=10"),
       col = 1:5, lty = 1:5, lwd = 2)


###不同的α下和不同自由度下的χ**2分布
curve(dchisq(x, 20), 0, 50, col = 1, lty = 1, lwd = 2,
      ylab = "p(x) of chisq(20)")
lines(c(qchisq(0.90, 20), qchisq(0.90, 20)), 
      c(-0.05, dchisq(qchisq(0.90, 20), 20)), 
      col = 2, lwd = 3, lty = 2)
qchisq(0.90,20)



## t分布
curve(dt(x, 1), -6, 6, ylab = "p(x)", lwd = 2, ylim = c(0, 0.4))
curve(dt(x, 2), -6, 6, col = 2, add = T, lwd = 2)
curve(dt(x, 5), -6, 6, col = 3, add = T, lwd = 2)
curve(dt(x, 10), -6, 6, col = 4, add = T, lwd = 2)
curve(dnorm(x), col = 6, add = T, lwd = 2, lty = 2)
legend("topright", legend = c("df=1", "df=2", "df=5", "df=10", "df=Inf"),
       col = c(1:4, 6), lty = c(rep(1, 4), 2), lwd = 2)

curve(dt(x, 4), -6, 6, col = 4, lwd = 2, ylim = c(0, 0.4), ylab = "p(x)")
curve(dnorm(x), col = 6, add = T, lwd = 2, lty = 2)
legend("topright", legend = c("t(4)", "N(0,1)"), col = c(4, 6), 
       lty = c(1, 2), lwd = 2)

qt(0.025,10)
qt(0.975,10)
qt(0.025,50)
qt(0.975,50)


## F分布
curve(df(x, 4, 1), 0, 4, ylab = "p(x)", lwd = 2, ylim = c(0, 0.8))
curve(df(x, 4, 4), 0, 4, col = 2, add = T, lwd = 2)
curve(df(x, 4, 10), 0, 4, col = 3, add = T, lwd = 2)
curve(df(x, 4, 4000), 0, 4, col = 4, add = T, lwd = 2)
legend("topright", legend = c("F(4,1)", "F(4,4)", "F(4,10)", "F(4,4000)"), 
       col = 1:4, lwd = 2)

qf(0.95,10,5)
qf(0.05,5,10)
1/qf(0.05,5,10)
qf(0.90,20,5)
qf(0.10,5,20)
1/qf(0.10,5,20)

